The Foehn (German) is a generic term for warm strong and often very dry downslope winds that descend in the lee of a mountain barrier. Originally applied to winds in the European Alps region, the term is now used for all similar winds. Foehn type winds (such as the chinook or the helm wind) are known for their rapid temperature rise, their desiccating effect and the rapid disappearance of snow cover.
The usual situation is this: A weather system is moving across a mountain range.
(1) Relatively stable, mild (e.g 20°C) but moist air starts at sea-level and has to cross the 3000m-mountain range situated parallel to it. The air is now forced to ascend and to glide up and over the windward mountain slopes. While initially decompressing and thus cooling at the dry adiabatic lapse rate of 1°C/100m, the air will eventually become saturated and the water vapour will condensate. Thus clouds will form and rain is setting in. The height where this happens is called condensation-level (at 600m a.s.l. in our example).
(2) Condensation releases heat and the further lifted air will cool somewhat slower now, lets say at a typical rate between 0.5 and 0.65°C/100m. This is called the wet or saturated adiabatic lapse rate. Once over the the mountain crest, the air will also have reached it's lowest temperature - somewhat around 1°C in our example.
(3) A so-called lee wave forms downwind of the obstacle. The downward motion of the initial wave forces the now-dry air to plummet from relatively high levels to the foothills, now warming by compression at the dry adiabatic lapse rate. Thus for every 100m drop in elevation, temperature raises 1°C again. The wind speed increases and the vigorous Foehn storm can easily reach gale force.
(4) Air temperature on the lee-side is now significantly higher than the same air on the upslope side of the mountains.
A Foehn like situation can last from less than an hour to several days. The high crest of the wave creates a distinctive elongated cloud parallel to the mountains, known as a föhn wall (aka. chinook arch or helm cloud). Further wave crests more distant to the obstacle form the popular lenticularis clouds.